Question

evaluate the limit as t approaches inifinity of $\lim_{t \to \infty} \frac{ \sqrt{t}+ t^{2} }{8t- t^{2} }$

Answer 1

$\displaystyle\lim_{t\to\infty}\frac{\sqrt t+t^2}{8t-t^2}=\lim_{t\to\infty}\frac{\dfrac1{t^{3/2}}+1}{\dfrac8t-1}=\frac1{-1}=-1$